Alfred Tarski . Polish logician, mathematician and philosopher, one of the most eminent representatives of the Lvov-Warsaw school. [1]
Summary
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- 1 Biographical synthesis
- 1 Trajectory
- 2 Contributions
- 3 References
- 4 Sources
Biographical synthesis
Born in Warsaw , the 14 of January of 1901 in a Jewish family and his original name was Alfred Tajtelbaum, name later changed to Alfred Tarski when converted to Catholicism and who had no interest whatsoever in maintaining their Jewish culture since that during these years the Second World War had broken out in the world and his condition as a Jew prevented him from accessing universities.
Trajectory
Upon his arrival in the United States , he began to work and make great contributions to mathematical sciences. Works on set theory, polyvalent logic, levels of language and metalanguage, and semantic concepts.
He was the author of “Introduction to the logic and methodology of the deductive sciences”, along with Aristotle , Gottlob Frege and Kurt Gödel . He is considered one of the greatest logicians of all time. Of the four, Tarski is one of the best mathematicians, the most prolific and the one with the most intense educational activity. Among his many and relevant disciples is Julia Robinson.
Contributions
In 1941 he published in English one of the most accredited manuals of logic, “Introduction to Logic and to the Methodology of Deductive Sciences”. He contributed to the maturity of standard logic —of the first order— by founding a set methodology of deductive theories on two bases: the notion of theory as a closed set of propositions under a notion of derivation through application of rules, and the development of a semantics based on the notions of satisfaction, truth and logical consequence.
His semantic methods, culminating in model theory developed in the 1950s and 1960s with his Berkeley disciples, radically transformed metamathematics, consolidating it as a strict science. The main idea is to replace the symbols of a certain theory by expressions of another theory so that the axioms of the first are translated into theorems of the other. The theory of models studies the properties that are inherited from some theories to others throughout these translations and compares the respective scopes of different theories. He was the inventor of one of the first proofs of the deduction theorem, with important applications in both logic and metallology.
Among many other additional aspects of his work is the introduction of the inaccessible cardinals whose existence allows the construction of models for set theory. He contributed in an important way to the foundation of model theory, a powerful tool of current logic: given a formal syntactic theory, many semantic models can be built where it is interpreted.
